{"id":"openai-math/The-maximal-triangular-Hilbert-transform-at-the-symmetric-point","pdf":"https://github.com/openai/math/blob/main/preprints/The-maximal-triangular-Hilbert-transform-at-the-symmetric-point-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-maximal-triangular-Hilbert-transform-at-the-symmetric-point-September-24-2026","tags":["harmonic-analysis","hilbert-transform","singular-integrals"],"score":0,"title":"The maximal triangular Hilbert transform at the symmetric point","domain":"Real and complex analysis","family":"082","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.CA","summary":"For arbitrary complex inputs in $`L^3(\\mathbb R^2)`$, we prove the pointwise maximal $`L^3\\times L^3\\to L^{3/2}`$ estimate for the triangular Hilbert transform, with the supremum over both hard truncation endpoints. The estimate yields joint almost-everywhere and L 3/2 convergence as the lower endpoint tends to zero and the upper endpoint tends to infinity. This also proves the conjectured scalar estimate at the symmetric point.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":true,"family_title":"Annular variation and dyadic absolute bounds for the triangular Hilbert transform"}